Topological-Antitopological Fusion and the Large N CP^N Model

Details Topological-Antitopological Fusion and the Large N CP^N Model Topological-Antitopological Fusion and the Large N CP^N Model

1993-12-12

arxiv.org/abs/hep-th/9312095v1

Nucl.Phys. B420 (1994) 243-267

Physics

High Energy Physics

High Energy Physics - Theory

24 pages (LaTeX), OUTP-93-24P and RU-93-56

Scientific paper

10.1016/0550-3213(94)90380-8

We discuss the large $N$ limit of the supersymmetric $CP^N$ models as an illustration of Cecotti and Vafa's $tt^*$ formalism. In this limit the `$tt^*$ equation' becomes the long wavelength limit of the $2D$ Toda lattice, an equation first studied in the context of self-dual gravity. We show how simple finite temperature and large $N$ techniques determine the relevant solution, and verify analytically that it solves the $tt^*$ equation, using Legendre transform techniques from self-dual gravity.

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